• Title, Summary, Keyword: semi-symmetric spaces

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RIEMANNIAN MANIFOLDS WITH A SEMI-SYMMETRIC METRIC P-CONNECTION

  • Chaubey, Sudhakar Kr;Lee, Jae Won;Yadav, Sunil Kr
    • Journal of the Korean Mathematical Society
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    • v.56 no.4
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    • pp.1113-1129
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    • 2019
  • We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric P-connection.

Symmetry Properties of 3-dimensional D'Atri Spaces

  • Belkhelfa, Mohamed;Deszcz, Ryszard;Verstraelen, Leopold
    • Kyungpook Mathematical Journal
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    • v.46 no.3
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    • pp.367-376
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    • 2006
  • We investigate semi-symmetry and pseudo-symmetry of some 3-dimensional Riemannian manifolds: the D'Atri spaces, the Thurston geometries as well as the ${\eta}$-Einstein manifolds. We prove that all these manifolds are pseudo-symmetric and that many of them are not semi-symmetric.

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Conformally Flat Quasi-Einstein Spaces

  • Chand De, Uday;Sengupta, Joydeep;Saha, Diptiman
    • Kyungpook Mathematical Journal
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    • v.46 no.3
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    • pp.417-423
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    • 2006
  • The object of the present paper is to study a conformally flat quasi-Einstein space and its hypersurface.

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GRADIENT RICCI SOLITONS WITH SEMI-SYMMETRY

  • Cho, Jong Taek;Park, Jiyeon
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.213-219
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    • 2014
  • We prove that a semi-symmetric 3-dimensional gradient Ricci soliton is locally isometric to a space form $\mathbb{S}^3$, $\mathbb{H}^3$, $\mathbb{R}^3$ (Gaussian soliton); or a product space $\mathbb{R}{\times}\mathbb{S}^2$, $\mathbb{R}{\times}\mathbb{H}^2$, where the potential function depends only on the nullity.

CLASSIFICATION OF CLIFFORD ALGEBRAS OF FREE QUADRATIC SPACES OVER FULL RINGS

  • Kim, Jae-Gyeom
    • Bulletin of the Korean Mathematical Society
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    • v.22 no.1
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    • pp.11-15
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    • 1985
  • Manddelberg [9] has shown that a Clifford algebra of a free quadratic space over an arbitrary semi-local ring R in Brawer-Wall group BW(R) is determined by its rank, determinant, and Hasse invariant. In this paper, we prove a corresponding result when R is a full ring.Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is non-degenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$(V,R) induced by B is an isomorphism), and with a quadratic mapping .phi.: V.rarw.R such that B(x,y)=1/2(.phi.(x+y)-.phi.(x)-.phi.(y)) and .phi.(rx) = $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U9R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$,.., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2 we reserve the notation [a $a_{11}$, $a_{22}$] for the space. A commutative ring R having 2 a unit is called full [10] if for every triple $a_{1}$, $a_{2}$, $a_{3}$ of elements in R with ( $a_{1}$, $a_{2}$, $a_{3}$)=R, there is an element w in R such that $a_{1}$+ $a_{2}$w+ $a_{3}$ $w^{2}$=unit.TEX>=unit.t.t.t.

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